Understanding Gaussian distribution

Today, I want to introduce a distribution that we already know, called Gaussian distribution . Gaussian distribution is a core distribution in probability theory, and Gaussian distribution is ubiquitous in machine learning, such as Gaussian model , Gaussian mixture model , Gaussian process and so on, which are all based on Gaussian distribution. As a basis for understanding the continuous stochastic variables and in-depth understanding of the extensive application of machine learning, Gaussian distribution is very necessary to learn.

Gaussian distribution is also called normal distribution, and the function form of the Gaussian distribution probability density function is deduced by the famous German genius mathematician, statisticians, physicist and astronomer Gauss. An important theorem related to Gaussian distribution is the central limit theorem , which has the following contents: The distribution of any distributions is Gaussian when the sample is large enough. The density function of the Gaussian distribution is

The mathematical expectation is equal to the position parameter, which determines the position of the distribution, its standard deviation is equal to the scale parameter, and determines the amplitude of the distribution. The Gaussian distribution of the probability density function curve is bell-shaped, so called bell-shaped curve , usually said the standard normal distribution is the Gaussian distribution. Next, we enter the most important part---the derivation of the probability density function of Gaussian distribution. There is a good paper that describes the complete derivation of the Gaussian distribution.

Paper Link:http://www.doc88.com/p-0814329057281.html

Then the expectation is deduced based on the probability density function of the Gaussian distribution. The process is as follows

Articles about Gaussian distributions: http://www.itongji.cn/article/111313452012.html

Understanding Gaussian distribution